An Exploration of Sequence A000975

Sequence A000975 in the Online Encyclopedia of Integer Sequences (OEIS) starts out 1, 2, 5, 10, 21, 42, 85, … . As of July 1, 2016, the description in the OEIS lists several characterizations of this sequence and numerous examples of instances where this sequence occurs. It also presents a “not yet proved” result, a conjecture, and an unanswered question concerning this sequence. In this paper we show that all of these proposed results are in fact true.